An increasingly visible irregular immigrant population, accompanied by increased immigration enforcement, can give rise to greater public concern over immigration even if overall immigrant flows are reducing, the paper adds.

UK Border Agency (Image: Steve Parsons/PA Wire)

It urges the Government to "inject a dose of honest realism, coming clean about the complexities and unintended consequences of immigration policy, about the control that it does have, but also the practical limits to that control".

Jonathan Thomas, SMF migration researcher and author of the report, said: "History suggests that people who expect ending free movement to take away their worries about immigration are going to be disappointed.

"Illegal immigration has not been a big part of British debate in recent years but the precedents suggest it could soon be high on the political agenda."

He added: "People who want to end free movement should be honest with the electorate about the possibility that it will create significant new challenges relating to illegal immigration.

"And people who support a liberal approach to immigration should engage constructively with the perfectly legitimate view that illegal immigration is a problem that policymakers should address."

In December, ministers unveiled plans for the biggest shake-up of the UK's immigration system in more than 40 years.

Under the proposals, outlined in a long-awaited White Paper, a new temporary work route will be created, the annual cap on skilled work visas will be scrapped, and employers wanting to sponsor overseas employees will no longer be required to carry out a "resident labour market test".

Officials insist it is not possible to accurately quantify the number of people in the country illegally.

In 2017, a former immigration enforcement chief claimed the figure was likely to run to more than a million.

Fourteen years ago, a Home Office assessment put the unauthorised migrant population living in the UK in 2001 at an estimated 430,000.